Description of the Workshop
The two day workshop deals with the numerical schemes for solution of the real life systems such as Numerical Weather Prediction, Cloud Bursting, Image Processing, Computational Fluids Flows of Manufacturing units, Machine Tool Ways etc. It also focuses on convergence, stability of matrix procedures which are the end product of any numerical approximation methods where complexity of performance of any iterative procedure is a big issue.
Handling large scale sparse systems through matrix factorisation for better approximate solutions of governing partial differential equations. At the end , we try to demonstrate matrix factorisation schemes using MATLAB, MATHEMATICA and Python Programs which are mostly open source.
Profile of the Instructor
Prof. Rao earned his Ph.D. in computational fluid dynamics from IIT Kanpur in 2001. Since then, he has been teaching various Mathematics and Computer Science courses, including Multivariable calculus, Numerical methods and specialised topics like Computational fluid dynamics and Artificial intelligence, Numerical Linear Algebra, Artificial Intelligence at BITS Pilani and IIT (ISM) Dhanbad for both UG and PG disciplines. His research spans applied areas such as Thrust bearing lubrication, Heat transfer, and High-speed lubrication, supported by funding agencies like UGC, ISRO, NBHM and ANF (Anusandhan Research Foundation). He has supervised 9 Ph.D. scholars and 32 postgraduate projects for both M. Tech, M.SC students. Prof. Rao also led the establishment of a supercomputing facility and has conducted popular NPTEL courses for Numerical Linear Algebra. He is known for his motivating, collaborative and innovative approach in Applied Mathematics & Computing areas.
Intended Audience & Eligibility
Intended Audience:
PhD Scholar, Scientists, University faculty members of engineering, science disciplines.
Eligibility:
Experience in handling software packages such as Matlab, Mathematica, Python, C Programming is desirable.
Module Details
1st March, 2025 – Day 1:
Module Name : Linear Algebra
Concepts Covered :
Floating Point Numbers, Errors Computations
Learning Outcomes :
How error computation takes place
Module Name : Stability of Algorithms
Concepts Covered :
Data predictions, types of data, Conditioning , LU factorisations
Learning Outcomes :
Data Types before processing for input
2nd March, 2025 – Day 2 :
Module Name : Numerical Solution of Linear Systems
Concepts Covered:
LU, QR, SVD etc for large scale data arising in Image processing, Weather Prediction, Cloud Bursting etc
Learning Outcomes:
Factorisation for easy numerical solutions
Module Name : Projections and Factorisations
Concepts Covered :
Special systems of large scale data predictive methods for possible input, pivoting, scaling etc
Learning Outcomes:
Conditioning, Pivoting for best possible numerical solutions and associated properties.
Certification Criteria
Attendance , MCQ’s and SAT are the criteria to obtain the certification
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